This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs between two distinct continuous distributions $F$ and $G$ on $\mathbb R$. The estimator is based on the order statistics of (possibly dependent) samples of $F$ resp. $G$. We prove the consistency and the asymptotic normality of our estimators. \begin{ it}Keywords:\end{ it} Central Limit Theorems- Generelized Wasserstein distances- Empirical processes- Strong approximation- Dependent samples.
Categories: math.ST stat.TH